for some constant \(B\)  and all \(w\in \lbrace w\,|\,{\sum _{i=1}^m \nabla f_i(w)}^2>\varepsilon \rbrace \) . Note that since the accuracy \(\varepsilon \)  can be chosen arbitrarily small, this condition is restrictive as it would effectively force \(B\rightarrow \infty \)  as \(\varepsilon \rightarrow 0\) , unless data distributions are similar across clients.  In other words, in scenarios where accurate solutions are pursued and when data distributions are heterogeneous, the analysis in [1]} dictates that all clients need to participate in each round (which is highly undesirable in FL) when such an assumption is imposed.
